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http://dx.doi.org/10.13067/JKIECS.2013.8.11.1749

Number of Different Solutions to x5+bx3+b2mx2+1=0 over GF(2n)  

Choi, Un-Sook (동명대학교 자율전공학부)
Cho, Sung-Jin (부경대학교 응용수학과)
Publication Information
The Journal of the Korea institute of electronic communication sciences / v.8, no.11, 2013 , pp. 1749-1754 More about this Journal
Abstract
Binary sequences of period $2^n-1$ are widely used in many areas of engineering and sciences. Some well-known applications include coding theory, code-division multiple-access (CDMA) communications, and stream cipher systems. In this paper we analyze different solutions to $x^5+bx^3+b^{2^m}x^2+1=0$ over $GF(2^n)$. The number of different solutions determines frequencies of cross-correlations of nonlinear binary sequences generated by $d=3{\cdot}2^m-2$, n=2m, m=4k($k{\geq}2$). Also we give an algorithm for determination of number of different solutions to the equation.
Keywords
Number of Solutions; Finite Fields; Trace Function; Cross-Correlation; Equation;
Citations & Related Records
Times Cited By KSCI : 5  (Citation Analysis)
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